Pore topology, volume expansion and pressure development in chemically-induced foam cements

Foam cement is an engineered lightweight material relevant to a broad range of engineering applications. This study explores the effects of aluminum chips on cement-bentonite slurry expansion, pressure development, and the evolution of pore topology. The terminal volume expansion under free-boundary conditions or the pressure build up under volume-controlled conditions are a function of the aluminum mass ratio, bentonite mass ratio, and aluminum chip size. X-ray CT images show that finer aluminum chips create smaller pores but result in a larger volume expansion than when larger sized chips are used; on the other hand, large chip sizes result in unreacted residual aluminum. Time-lapse CT images clearly show the sequence of processes which lead to the development of foam cement: gas bubble nucleation, bubble growth, capillary-driven grain displacement enhanced by the presence of bentonite, coalescence, percolation, gas leakage and pore collapse. These results illustrate the potential to customize the mixture composition of chemically-induced gassy cement to control expansion and pressure build up, and to minimize percolating discontinuities and gas release.


Supplementary Appendix A. Porosity of Foam Cement
Final Porosity nf. Let us consider a cement paste that has an initial volume Vo composed of volume of void VV and volume of solid VS (i.e., Vo = VS + VV). Figure A1. Simplified phase diagram for foam cement.
The initial porosity no is the ratio between volume of void VV and the initial volume Vo Assuming the initial degree of saturation So = 100%, the initial porosity no is where VV = VW and subscripts W, C, B, and A indicate water, cement, bentonite, and aluminum respectively. In terms of mass densities ρ = M/V, where the parameter μ denotes the mass ratio between the mass of each component and the mass of cement MC (e.g., water-cement ratio μWC = MW/MC), and the specific gravity of each phase is G = ρ/ρw. After foaming, the volume expansion ratio β relates the final volume Vf of foam cement to the initial volume Vo where VG indicates the volume of gas bubbles. Then, the final porosity nf after volume expansion is the ratio between (VG + VV) and Vf Note that this first order approximation assumes that the volume of solid remains constant.
For example, consider a cement paste that has water-cement mass ratio μWC = 1, bentonite-cement mass ratio μBC = 0.08, and aluminum-cement mass ratio μAC = 0.04 (see Table 1). Specific gravities are: GC = 3.15 for cement, GB = 2.7 for bentonite and GA = 2.7 for aluminum. Then, the initial porosity is no = 0.734 for all cases in Figure 2c (Equation A-4). For the cement paste with aluminum chip size d50 = 0.04mm, the volume expansion ratio is β = Vf/Vo = 1.5 (see Figure 2c). Then, the final porosity is

Supplementary Appendix B. Pressure Generation
Let us make the following assumptions to obtain a first-order estimate of pressure generation (See Innocentini et al. 2003 for a similar analysis): • Constant temperature and constant slurry volume Vo= constant, i.e., the volume of liquid and solid in the slurry does not change during the reaction.
• The empty cell volume Vcell -Vo is initially filled with air. Air and the generated hydrogen will occupy this volume after the reaction.
• Assuming Dalton's law, the final pressure created by the gas mix will be the sum of their partial pressures: Pmax= Pair + PH2. Air does not experience volume change thus Pair remains at Pair= 1atm; therefore, the change in Pmax is controlled by the partial pressure of hydrogen PH2.
• The change in hydrogen pressure with respect to volume under constant temperature follows Boyle-Mariotte's law for ideal gas behavior without correction for molecular size (i.e., Van der Waals equation -Note: precise equations of state for hydrogen gas typically involves the integration along the pressure-temperature trajectory). Then, for hydrogen only: where 1atm refers to one atmosphere. The density of hydrogen at one atmosphere is ρ1atm= Then, the maximum pressure in the cell is the sum of partial pressures When the fraction of reacted aluminum is λ= Mreact / MA, then the generated pressure becomes ( ) where the approximation on the right applies when the pressure generation is high.